Hydrodynamics of helical bacteria with polar flagella

Amphitrichous bacteria swim by coordinating the rotation of two helical flagella, each anchored at opposite poles of a spirillum-shaped cell body. The motility modes of these cells depend on the combination of rotational directions of the two bipolar flagella and the magnitude of the motor torque. In this study, we develop a mathematical model of an amphitrichous bacterium to investigate its swimming mechanisms. Flagellar motor rotation serves as the driving source for propulsion in a viscous fluid, and the hydrodynamics of the cell is governed by the incompressible Stokes equations under the constraint that the net force and torque on the fluid are zero at all times. Our simulations reproduce experimentally observed swimming behaviors when appropriate choices of material properties and geometrical parameters are specified for both the flagella and the cell body. Furthermore, the results reveal that swimming is more efficient when the cell body and the flagella possess opposite helical handedness compared to configurations with the same handedness.